COMPUTATIONAL STUDIES ON FORMATION AND PROPERTIES OF CARBON NANOTUBES Weiqiao Deng, Jianwei Che, Xin Xu, Tahir Çagin, and William A Goddard, III Materials and Process Simulation Center, Beckman Institute, 139-74, California Institute of Technology, Pasadena, California, USA ABSTRACT The discovery of lower dimensional forms of Carbon with unique mechanical and electronic properties has generated new possibilities in many areas of technology especially in nanotechnology. Recent emergence of some nanoscale device applications show how this potential is turning into a reality. Over the years, we have employed various levels of theory to study the structure and properties of carbon based materials for nanoscale applications. In this paper, we present two new theoretical studies. We present a study on the transition metal catalyzed growth of single wall carbon nanotubes. In the second study, we investigate the relation between mechanical deformation and excess charge in order to understand how introducing and controlling the charge at various locations might modify the mechanical and acoustical properties of carbon nanotubes. We demonstrate that introducing excess charges into single wall carbon nanotubes can lead mechanical deformations that do mechanical work. The results suggest a wide range for practical applications, such as NEMS, acoustic sensors and nanoactuators. INTRODUCTION The peculiar chemistry of carbon results in diverse forms of structure: the 3-dimensional network of diamond and the 2- dimensional sheets of graphite have been known through the ages. The discovery of lower dimensional forms of Carbon with unique mechanical and electronic properties has generated new possibilities in many areas of technology especially in nanotechnology. Recent emergence of some nanoscale device applications show how this potential is turning into a reality. Over the years, we have been using ab initio quantum chemistry, density functional theory and molecular dynamics methods to study the structure and properties of carbon based materials for nanoscale applications. The applications such as; a) Structural and mechanical properties of nanotubes, (refs 1-3); b) Tribological properties of carbon for NEMS applications (ref 4); c) Thermal transport properties of nanotubes and carbon based heterostructures (refs 5-6), and d) Formation of fullerenes, (ref 7) have appeared elsewhere. In this paper, we will present two new theoretical studies. Over the past several years a large number of synthetic procedures for the production of Carbon nanotubes have been developed. Since the electronic properties of carbon nanotubes depend on structure the control of growth is essential. Theoretical studies of growth mechanisms may shed some light on how to control the growth. We first present a study on the transition metal catalyzed growth of single wall carbon nanotubes. In the second application, we investigate the relation between mechanical deformation and excess charge in order to understand how introducing and controlling the charge at various locations might modify the mechanical and acoustical properties of carbon nanotubes. We demonstrate that introducing excess charges into single wall carbon nanotubes can lead mechanical deformations that do mechanical work. The results suggest a wide range for practical applications, such as NEMS, acoustic sensors and nanoactuators. MECHANISM OF TRANSITION METAL CATALYZED GROWTH OF SINGLE-WALL CARBON NANOTUBE Introduction Single-wall carbon nanotubes have been produced in the outflow of a carbon arc discharged method (ref 8) and in even with higher yield by the laser vaporization technique (refs 9-12) and more recently through chemical vapor deposition (ref 13). The transition metal catalysts such as Ni and Co are known to play important role in all of these methods. In the laser vaporization assisted growth, the concentration of metal catalyst in the graphite is very low (< 1%). The high temperatures in the experiment suggest that the catalyst may affect the growth as single atoms.
In 1997, Lee et al proposed a growth mechanism (ref 14). In this mechanism, the mobile Ni catalyst atoms are absorbed at the growth edge of SWCN where they prevent the formation of carbon pentagons and catalysis continues through formation of carbon hexagons. However, Froudakis group provided another mechanism (ref. 15): Ni atoms don t attach to the edge of the growth font. It actually first creates and stabilizes the defects in nanotube and then the incoming carbon atoms anneal the Ni-stabilized defects by freeing the Ni atom back to the catalytic cycle. These two mechanisms are contradicting. Besides this apparent contradiction, there still are some unsolved problems that need to be addressed. First, in the growth, what is the difference in the growth mechanisms with or without metal? Second, can the existing mechanisms explain why a metal works, while another metal does not work? Third, what is the determining step in a metal catalyzed growth of carbon nanotube? Fourth, where, at the edge or on the wall, does the metal atom locate during the growth? Theoretical model Here, we present results of a detailed theoretical study of the dynamical interaction between the Ni, Co, Pt and Cu catalysts and SWCN with a view towards an understanding of the nanotube growth mechanism and a detailed discussion on the unresolved problem above. Our calculations are based on first principle - density functional theory, as implemented in the Jaguar code, for a tube fragment with a metal atom attached. The B3LYP are used to describe exchange and correlation. We start with a (10,10) nanotube. The studied fragment is cut from a (10,10) nanotube structure and fixing the edge atoms (which are neutralized by H atom) to keep the curvature of the structure. Result and discussion First question to address is whether the role of the metal catalyst is a necessary prerequisite for the formation of single-wall nanotubes. In order to understand this issue, the mechanism of termination of nanotube in absence of metal atoms is undertaken. In Figure 1, we can see the two pathways while carbon atoms grow on the edge of nanotube. One pathway is to form a defect with two hexagons and two pentagons called 6,6,5,5 defect, consequently, after more and more defects are formed, the tip of nanotube is closed. Another pathway is that these two pentagons rearrange to form two hexagons and then the growth will proceed. The results show that for pathway 1 the energy will drop down by 81.9 kcal/mole and for pathway 2 the energy will go down by 51.7 kcal/mole. The large energy difference between these two pathways allows us to believe that in the absence of metal atoms the growth will be terminated immediately. This is in favor of Froudakis mechanism: The metal must attach on the edge of the nanotube growth front and prevents the defect formation. Second, we discuss the detailed catalytic mechanism with catalyst atoms to avoid the defect formation. First, we explore whether the Ni atom affects the growth. Our calculations show that Ni atom neither destroys the pentagon to form hexagon nor stabilizes the hexagon ring, because both are energetically unfavorable. For the former case, we started the simulation by inserting the Ni atom into a pentagon to form hexagon. This procedure is energetically unfavorable, which required energy of 12.4 kcal/mole. This means that Ni atom prefers to sit above the pentagon ring without break it. For the later case, the calculations indicate the arrangement to be energetically favorable with an energy gain of 27.2 kcal/mole without Ni catalyst and with an energy gain of 24.6 kcal/mole with Ni catalyst. The outcome of this calculation shows that the arrangement is not benefited from Ni metal atoms involve at the adjacent site. These results are in line with Lee s mechanism by concluding that Ni atoms don t prevent the pentagon formation or assist the assembly of carbon hexagons at the growing edge. Based on this, we provide a new mechanism shown in Figure 2. It says that Ni atoms block the adjacent sites of pentagon to prevent the defect formation. Ni atom can anneal the existed defects. Figure 2a shows that when carbon atoms come in, Ni atoms block both adjacent sites of the other sites so that pentagon carbon ring just is able to rearrange as hexagon ring that is energetically favorable, i.e, it reduces 24.60kcal/mole. Figure 2b indicate how a Ni atom anneals the defect. After Ni atom attaches the edge of the nanotube growth font, it will rearrange with carbon rings into several possible structures: structure 1-5 in Figure 2b. For growth, the structure (1) and (3) (4) are not helpful for annealing defect because the pentagons in the structure are not destroyed. At the other hand, structure (2) and (5) are good for anneal defects. We compare the energies of these structures and determine which structure the reaction path is trapped. For Ni metal atoms, structure (2) is the most stable one that will lead to an annealing pathway. Therefore, our mechanism successfully explains the Ni catalyst effect of nanotube growth. We also study the catalysis effect of other metals such as Co, Pt and Cu. In the table 1, we give a summary of these metals. Based on our calculation results, it shows that Co does work, Pt and Cu don t work, which is in good agreement with the experiments.
Conclusion Based on first principle calculation, we study the microscopic mechanism of single-wall carbon nanotubes growth by using the laser vapor deposition technology. By arguing the previous mechanism, we provide a new one here. It says that metal catalysts atom absorbed at the growth edge will block the adjacent growth site of pentagon and thus avoid the formation of defect. Metal catalysts can also anneal the existed defects. Additionally, our results show that the nanotube growth will terminate in the absence of metal catalysts and also explain why Pt and Cu are not good catalysts. Table 1 Relative energies (kcal/mole) of various metal cluster structures in figure 2b Ni Co Pt Cu (1) bad for annealing -19.65-1.11-27.34 (2) good for annealing -24.24-14.34 22.82-17.00 (3) bad for annealing -9.55 2.25 41.11-15.30 (4) bad for annealing 0.0 0.0 0.0 0.0 (5) good for annealing -5.66 9.8 2.13-7.26 (a) DE 1 = -81.9 kcal/mole (b) DE 1 = -51.7 kcal/mole Figure 1. The nanotube grows at the absence of metal catalysts. Pathway (a) is closure pathway; Pathway (b) is continue growth pathway. The colorful carbon atoms are our cluster model. E = -24.60 kcal/mole Figure 2a. The Ni atoms block adjacent site of pentagon to avoid the defect formation. The darker atoms are Ni atoms.
(1) (2) (4) (5) (3) Figure 2b. Metal Ni catalysts can anneal the formed defect. The darker atoms are Ni atoms. CHARGE EFFECTS ON MECHANICAL PROPERTIES OF CARBON NANOSTRUCTURES Introduction Over the past decade both theory and experiments have shown that carbon nanotubes have both unique electronic properties (e.g. it may be semiconducting or metalic depending on the charality) and extreme mechanical strength (e.g. tensile modulus ~1000 GPa). Consequently, there is considerable interest in designing and manufacturing functional devices and novel composite materials based on carbon nanotubes. In particular we consider here how introducing and controlling charges might modify the mechanical properties of carbon structures. The smaller nanostructures are moderate size molecules. To understand the systematic behavior of carbon nanotube s electronic and mechanical coupling, we started with the smallest molecule that resembled carbon nanotube structure, i.e. benzene. While the expansion of benzene molecule approaches the limit of graphene structure, we believed that the electro-mechanical coupling in graphene is in close resemblance to that in carbon nanotube. We will see this behavior later in our calculations. Results and Discussion Staring from benzene, we investigated naphthelene, pyrene, coronene, intercalated graphite, and single walled carbon nanotubes. Based on group theory, we know that the two HOMOs and two LUMOs of benzene are degenerate. In each PI MO, we can characterize the bonding between atoms by looking at the phase of their 2p orbital. When the two adjacent orbitals have opposite phase, an anti-bonding dominates the interaction between them in that specific MO. On the contrary, the same phase orbital generates bonding forces. Consequently, an electron in anti-bonding form will elongate the distance between two adjacent atoms, while an electron in bonding form will shrink the distance. The picture in the presentation clearly shows the structural change with respect to charging into different MOs. In larger molecules such as pyrene and coronene, we also observed the similar behavior. A similar system at large spatial scale is intercalated graphite. The quantum calculations for periodic systems were carried out using CASTEP. When positive charges are injected into the graphite crystal, the graphite sheets tend to shrink. On the other hand, negative charges make the graphite to expand. The structural deformation is mainly caused by the change in electronic structure rather than Coulomb interaction. In other words due to the filling of electrons in anti-bonding/conduction band or holes in bonding/valence band. Coulomb force is independent of charge signs. In addition, Coulomb interaction depends on charges in the quadratic order. For the intercalated graphite, we also found that AA stacking structure is more stable than AB stacking in agreement with experimental observations. Similar to intercalated graphite, carbon nanotubes also exhibit charge induced structural deformations. For single walled carbon nanotube, we chose (5,5) tube as an example. Although it has very small size, we believe that the results can demonstrate the essence of electro-mechanical coupling. The simulation cell consisted of two layers of
(5,5) unit cell. Either electrons or holes are filled into corresponding bands, and a uniform background charge is used to neutralize the total simulation box. From our calculations, we also found that positive charge tends to shrink 2.49 15 Along Tube Peoriodicity (Angstrom) 2.48 2.47 2.46 2.45 2.44 2.43 2.42 Cell Constant (Angstrom) 14 13 12 11 10 9 Cell constant a Cell constant b 2.41-3 -2-1 0 1 2 3 4 Charge Transfer (e) 8-4 -3-2 -1 0 1 2 3 4 Charge Transfer (e) Figure 3. Deformation as a function of charge transfer: Left deformation in the tube direction, Right deformation in the lateral directions. the tube and the tube tends to expand under negative charging. The reason is very similar to intercalated graphite. The charge injected into valence or conduction band caused the electronic structure to shift, and this shift is charge sign dependent. Intuitively, it can be viewed as new electronic structure under screened nuclear cores. In addition to the deformation along tube axis, we also saw the change in cell length in nanotube bundles. Although LDA usually does not give accurate results for nonbond interactions such as van de Waals forces, we think that the change in the lateral directions is mainly caused by the Coulomb forces. As it can be seen in electrostatic potential map, the inter tube space is mainly electronegative. When a charge variation is introduced, the inter-tube repulsion due to charge variations in positive core is on the second order, and the first order interaction is between the charge variation and the electrostatic potential. Therefore, the bundle size also shrinks or expands due to different type of charges. Figure 4. Electron density map In summary, we find that introducing excess charges into nanotubes can lead to mechanical deformations that do mechanical work in agreement with experiments by Baughman et. al. (ref 16). These results suggest a wide range of practical implications, including the design of nano-electronic-mechanical systems (NEMS) and nano-actuators.
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